{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ACFLK3YOPCZ7Y6NK2J7EB26AUX","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"1b1a552533789bc307f537f969343f94f77185135b1e9639654f84c5c8340d94","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-04-02T18:06:02Z","title_canon_sha256":"c01b8aabf2ce99133d8e1153a9bb9f543c0c65b9ab8d27d87dd6abf738468f85"},"schema_version":"1.0","source":{"id":"1804.00679","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.00679","created_at":"2026-05-18T00:06:20Z"},{"alias_kind":"arxiv_version","alias_value":"1804.00679v2","created_at":"2026-05-18T00:06:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.00679","created_at":"2026-05-18T00:06:20Z"},{"alias_kind":"pith_short_12","alias_value":"ACFLK3YOPCZ7","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"ACFLK3YOPCZ7Y6NK","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"ACFLK3YO","created_at":"2026-05-18T12:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:a0bbd0d90227b5fe280d353b9cb462da42d7868b95f08e6384a03e9bde89d1ed","target":"graph","created_at":"2026-05-18T00:06:20Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We study the BPS invariants for local del Pezzo surfaces, which can be obtained as the signed Euler characteristic of the moduli spaces of stable one-dimensional sheaves on the surface $S$. We calculate the Poincare polynomials of the moduli spaces for the curve classes $\\beta$ having arithmetic genus at most 2. We formulate a conjecture that these Poincare polynomials are divisible by the Poincare polynomials of $((-K_S).\\beta-1)$-dimensional projective space. This conjecture motivates upcoming work on log BPS numbers.","authors_text":"Jinwon Choi, Michel van Garrel, Nobuyoshi Takahashi, Sheldon Katz","cross_cats":["hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-04-02T18:06:02Z","title":"Local BPS Invariants: Enumerative Aspects and Wall-Crossing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.00679","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:e09a9f10112e3c64037d1a74cdb578d5fadae3abfd5d708f76c739da4b283cdc","target":"record","created_at":"2026-05-18T00:06:20Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"1b1a552533789bc307f537f969343f94f77185135b1e9639654f84c5c8340d94","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-04-02T18:06:02Z","title_canon_sha256":"c01b8aabf2ce99133d8e1153a9bb9f543c0c65b9ab8d27d87dd6abf738468f85"},"schema_version":"1.0","source":{"id":"1804.00679","kind":"arxiv","version":2}},"canonical_sha256":"008ab56f0e78b3fc79aad27e40ebc0a5f871acf576577d549f52665c29894e9a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"008ab56f0e78b3fc79aad27e40ebc0a5f871acf576577d549f52665c29894e9a","first_computed_at":"2026-05-18T00:06:20.393432Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:20.393432Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M+TbvuV6aYaxAa2t0KQIodQLuThRu8hw39KryfT7VmwqppmFI9B9hzqsg0K+F3mLfc98nEHU2/xm0plyjHyjAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:20.393913Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.00679","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e09a9f10112e3c64037d1a74cdb578d5fadae3abfd5d708f76c739da4b283cdc","sha256:a0bbd0d90227b5fe280d353b9cb462da42d7868b95f08e6384a03e9bde89d1ed"],"state_sha256":"23b8e70aca59c3b9dd0d02341811ad5b8f2c6bc64c56401ce02a86947ca34726"}